
'''simple docstring'''





from __future__ import annotations

import math
from collections.abc import Callable







def snake_case_     (					lowercase__   ,       lowercase__   ,       lowercase__   ,       lowercase__ = 1_0_0   ,       ):
  UpperCAmelCase__      :					Dict				       =							x_start
  UpperCAmelCase__      :					Optional[Any]				       =							fnc(lowercase__		)
  UpperCAmelCase__      :					Tuple				       =							0.0

  for _ in range(lowercase__		):
    # Approximates curve as a sequence of linear lines and sums their length
    UpperCAmelCase__      :					Optional[Any]				       =							(x_end - x_start) / steps + xa
    UpperCAmelCase__      :					Optional[Any]				       =							fnc(lowercase__		)
    length += math.hypot(xa - xa   ,       fxa - fxa		)

    # Increment step
    UpperCAmelCase__      :					Union[str, Any]				       =							xa
    UpperCAmelCase__      :					Dict				       =							fxa

  return length


if __name__ == "__main__":







      def snake_case_     (					lowercase__		):
        return math.sin(1_0 * x		)

      print("""f(x) = sin(10 * x)""")
      print("""The length of the curve from x = -10 to x = 10 is:""")
      SCREAMING_SNAKE_CASE     =       1_0
      while i <= 1_0_0_0_0_0:
            print(F'With {i} steps: {line_length(f, -1_0, 1_0, i)}')
            i *= 1_0




import functools
from typing import Any


def 	lowerCamelCase					(	UpperCamelCase     :				str			,       UpperCamelCase     :				list[str]							)   ->    bool:

		# Validation
		if not isinstance(UpperCamelCase			,       UpperCamelCase							) or len(UpperCamelCase							) == 0:
				raise ValueError('the string should be not empty string'							)

		if not isinstance(UpperCamelCase			,       UpperCamelCase							) or not all(
		    isinstance(UpperCamelCase			,       UpperCamelCase							) and len(UpperCamelCase							) > 0 for item in words							):
				raise ValueError('the words should be a list of non-empty strings'							)

		# Build trie
		_lowerCamelCase				   =  {}
		_lowerCamelCase				   =  'WORD_KEEPER'

		for word in words:
				_lowerCamelCase				   =  trie
				for c in word:
						if c not in trie_node:
								_lowerCamelCase				   =  {}

						_lowerCamelCase				   =  trie_node[c]

				_lowerCamelCase				   =  True

		_lowerCamelCase				   =  len(UpperCamelCase							)

		# Dynamic programming method
		@functools.cache
		def is_breakable(UpperCamelCase     :				int							) -> bool:
				if index == len_string:
						return True

				_lowerCamelCase				   =  trie
				for i in range(UpperCamelCase			,       UpperCamelCase							):
						_lowerCamelCase				   =  trie_node.get(string[i]			,       UpperCamelCase							)

						if trie_node is None:
								return False

						if trie_node.get(UpperCamelCase			,       UpperCamelCase							) and is_breakable(i + 1							):
								return True

				return False

		return is_breakable(0							)


if __name__ == "__main__":
				import doctest

				doctest.testmod()